Child-resistant container closures are known in the art. Such closures typically have a nested two-cap construction, including a base cap for sealing a container opening and a cover cap that captures the base cap. The base cap threads onto a neck of the container about the opening. Cooperating features disposed on an inner portion of the cover cap and an outer portion of the base cap enable selective engagement between the base cap and the cover cap, such that a single rotational action is sufficient to install the closure onto the container while a combined rotational and pushing and/or squeezing action is required to remove the closure from the container. In practice, when the cover cap is rotated in a first direction so as to thread the base cap onto the container neck, the cover cap and the base cap reliable engage and rotate in tandem, but when the cover cap is rotated in second a direction so as to unthread the base cap from the container neck, the cover cap must be further manipulated (e.g., by pushing downward on the cover cap or squeezing a portion of the cover cap while rotating) to cause the base cap to rotate in tandem with the cover cap. If the cover cap is rotated in the second direction without further manipulating the cover cap, the closure the closure will not open the container.